Course Log
Here you will find information about the material that was already covered or will be covered in the next few lectures.
Covered | |
---|---|
Fri, Apr 19: | [M] §30 The Differential Operator, §32 The Action of a Differentiable Map |
Mon, Apr 17: | Overview of Midterm Exam 2 |
Mon, Apr 15: | [M] §29 Tangent Vectors and Differential Forms |
Fri, Apr 19: | [M] §27 Alternation Tensors, §28 Wedge Product |
Wed, Apr 17: | [M] §26 Multilinear Algebra, §27 Alternation Tensors |
Mon, Apr 15: | Review for Midterm Exam 2 |
Fri, Apr 12: | [M] §25 Integration of a Function over a Manifolds |
Wed, Apr 10: | [M] §24 Examples, §25 Integration of a Function over a Manifolds (start) |
Mon, Apr 8: | [M] §24 The Boundary of a Manifold |
Fri, Apr 5: | [M] §23 Manifolds in $\mathbb{R}^n$ (cont.) |
Wed, Apr 3: | [M] §16 Partitions of Unity (cont.) §23 Manifolds in $\mathbb{R}^n$ |
Mon, Apr 1: | [M] §16 Partitions of Unity |
Fri, Mar 29: | [M] §15 Exhaustion by Compacts, Improper Integrals, §16 Bump Functions |
Wed, Mar 27: | [M] §22 Volume of a Parametrized Manifold, Integration on a Parametrized Manifold |
Mon, Mar 25: | [M] §21 Volume of the Parallelopiped |
Fri, Mar 22: | [B] §45 Change of Variables (Strong Form) |
Wed, Mar 20: | [B] §45 Change of Variables |
Mon, Mar 18: | [B] Overview of Midterm Exam 1, §45 Transformation by Nonlinear Maps, Jacobian Theorem |
Fri, Mar 15: | Spring Break |
Wed, Mar 13: | Spring Break |
Mon, Mar 11: | Spring Break |
Fri, Mar 8: | Cancelled (because of Midterm Exam 1) |
Wed, Mar 6: | [B] §45 Transformation by Linear Maps, Transformation by Nonlinear Maps (start) |
Mon, Mar 4: | [B] Review for Midterm Exam 1 |
Fri, Mar 1: | [B] §45 Transformations of Sets with Content |
Wed, Feb 27: | [B] §44 Integral as Iterated Integral, §45 Transformations of Sets with Content (start) |
Mon, Feb 25: | [B] §44 Further Properties of Integral, Mean Value Theorem |
Fri, Feb 22: | [B] §44 Sets with Content (cont.), Characterization of Content Function |
Wed, Feb 20: | [B] §43 Properties of Integral (cont.), Existence of Integral, §44 Sets with Content (start) |
Mon, Feb 18: | [B] §43 Darboux’s upper and lower integrals (cont.), Riemann’s Criterion for Integrability, Properties of Integral |
Fri, Feb 15: | [B] §43 Definition of Integral, Darboux’s upper and lower integrals (Project 43.$\alpha$) |
Wed, Feb 13: | [B] §43 Content zero |
Mon, Feb 11: | [B] §42 Inequality Constraints, Examples |
Fri, Feb 8: | [B] §42 Lagrange’s Theorem (finish), Examples |
Wed, Feb 6: | [B] §42 Second Derivate Test (finish), Extremum Problems with Constraints, Lagrange’s Theorem (start) |
Mon, Feb 4: | [B] §42 Local (Relative) Extrema, First Derivative Test, Second Derivative Test (start) |
Fri, Feb 1: | [B] §41 Implicit Function Theorem |
Wed, Jan 30: | Cancelled (Wind Chill Emergency) |
Mon, Jan 28: | [B] §41 Inversion Theorem, Implicit Function Theorem (start) |
Fri, Jan 25: | [B] §41 Surjective Mapping Theorem, Open Mapping Theorem |
Wed, Jan 23: | [B] §41 Class $C^1$, Approximation Lemma, Injective Mapping Theorem |
Mon, Jan 21: | No class (MLK day) |
Fri, Jan 18: | [B] §40 Higher Derivatives, Taylor’s Theorem, §41 Class $C^1$ (start) |
Wed, Jan 16: | [B] §40 Interchange of the Order of Differentiation |
Mon, Jan 14: | [B] §40 Chain rule, Mean Value Theorems |
Fri, Jan 11: | [B] §39 Jacobian, existence of the derivative, §40 Algebraic properties of derivatives |
Wed, Jan 9: | [B] §39 Directional and partial derivatives, the derivative |
Mon, Jan 7: | [B] §39 The Derivative (start), §21 Linear functions |